import pandas as pd
from sympy.solvers import solve
from sympy import Symbol
import plotly.graph_objs as go
import plotly.express as px

surface = 500000 #m^2
Q = 150 #m^3/s into zoozanaghe
#Qouts=[Q for i in range(13)]
b = 40 #m and 1V:1.5H
g = 9.81
# hydrograph 6hrs after flood ? #ravesh puls(!)

Time = [0.5 * i for i in range(13)]
Qs = [150, 175, 220, 300, 380,
      375, 305, 235,200, 180,
      162, 150, 150]
df = pd.DataFrame({'zaman(hr)': Time,
              'debi_voroodi(m^3/s)': Qs})
''',
              'debi_khorooji(m^3/s)': Qouts})'''
df = df.transpose()
df

See Full Dataframe in Mito

	0	1	2	3	4	5	6	7	8	9	10	11	12
zaman(hr)	0.0	0.5	1.0	1.5	2.0	2.5	3.0	3.5	4.0	4.5	5.0	5.5	6.0
debi_voroodi(m^3/s)	150.0	175.0	220.0	300.0	380.0	375.0	305.0	235.0	200.0	180.0	162.0	150.0	150.0

puls method

in each time step: $I.\Delta T - O.\Delta T = \Delta V $

steep:

$ Q = A*V $

and:

$ A = 1.5y_c^2 + 40y_c $ also $ V_c = \sqrt{gy_c} $

import IPython.display as ID
fig = ID.Image("eq_solve.png")
ID.display(fig)

yc = 1.09
A = lambda y: 1.5*y**2 + 40 * y
T= lambda y: b + 3 * y
D = lambda y: A(y) / T(y) 
Hc = yc + (D(yc)/2)
Hc

1.6144066327709732

Heads = [Hc, 2, 2.5, 3, 2.5, 4]
#----------------------------------------------------------------
Ys = []
for i in Heads:
    y = Symbol('y')
    javab = solve(y + (D(y)/2) - i,y)
    Ys.append(float(javab[1]))
#----------------------------------------------------------------
Vs = [(g * i)**0.5 for i in Ys]
#----------------------------------------------------------------
Q_out = []
for i in range(len(Ys)):
    area = A(Ys[i])
    speed = Vs[i] 
    Q_out.append(area*speed)
#----------------------------------------------------------------
Vol = []
V = 0
Vol.append(V)
for i in range(len(Heads)):
    try:
        H1 = Heads[i]
        H2 = Heads[i+1]
        V = (surface * (H2 - H1)) + V
        Vol.append(V)
    except:
        pass
#----------------------------------------------------------------
VperdeltaT = [(i / (0.5 * 60 * 60)) for i in Vol]
#----------------------------------------------------------------
N = []
for i in range(len(Q_out)):
    O2vom = Q_out[i] / 2
    n = O2vom + VperdeltaT[i]
    N.append(n)
df1 = pd.DataFrame({'Heads': Heads, 'Y(c)': Ys, 'V(c)': Vs,
                    "Q out": Q_out, 'V': Vol, "V / DT": VperdeltaT, "N": N})
df1

See Full Dataframe in Mito

	Heads	Y(c)	V(c)	Q out	V	V / DT	N
0	1.614407	1.090000	3.270000	148.399630	0.000000e+00	0.000000	74.199815
1	2.000000	1.354141	3.644740	207.444723	1.927967e+05	107.109269	210.831630
2	2.500000	1.698659	4.082137	295.034500	4.427967e+05	245.998158	393.515408
3	3.000000	2.045338	4.479371	394.581598	6.927967e+05	384.887046	582.177846
4	2.500000	1.698659	4.082137	295.034500	4.427967e+05	245.998158	393.515408
5	4.000000	2.744762	5.189038	628.345991	1.192797e+06	662.664824	976.837820

px.line(x = N, y = Q_out)

import IPython.display as ds
ds.Image('soal2_fited.png')

import numpy as np
x = np.array(df1.N)
y = np.array(Q_out)
m, b = np.polyfit(x, y, 1)
m, b

(0.5352112294358141, 93.44308191158399)

O = lambda N: m * N + b

meanI = []
for i in range(len(Qs)):
    try:
        I1 = Qs[i]
        I2 = Qs[i+1]
        meanI.append((I2 + I1) / 2)
    except:
        pass
#----------------------------------------------------------------
O0 = Qs[0]
N1 = N0 = O0 / 2
Os = [O0]
Ns = []
dN = meanI[0] - O0
#----------------------------------------------------------------

for i in range(len(meanI)):
    Ibar = meanI[i]
    dN = Ibar - O0
    N1 = N1 + dN
    O0 = O(N1)
    Os.append(O0)

px.line(Os)

final = pd.DataFrame({"debi khorooji" : Os, 'debi voroodi': Qs})
final

See Full Dataframe in Mito

	debi khorooji	debi voroodi
0	150.000000	150
1	140.274064	175
2	170.902028	220
3	218.588263	300
4	283.569188	380
5	333.842013	375
6	337.137837	305
7	301.204913	235
8	256.405103	200
9	220.864346	180
10	194.176388	162
11	173.743957	150
12	161.035924	150

fig = go.Figure()
fig.add_trace(go.Scatter(x = Time, y = Qs, name = 'Q_in'))
fig.add_trace(go.Scatter(x = Time, y = Os, name = 'Q_out'))
fig.update_layout(
    title="Hydrograph",
    xaxis_title="zaman(s)",
    yaxis_title="debi(m^s/s",
    legend_title="jaryan",
    font=dict(
        family="Courier New, monospace",
        size=18,
        color="RebeccaPurple"
    )
)